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# If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x

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Math Expert
Joined: 02 Sep 2009
Posts: 64222
If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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20 May 2018, 13:22
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65% (hard)

Question Stats:

53% (01:27) correct 47% (01:15) wrong based on 234 sessions

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GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

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Posts: 1153
Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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20 May 2018, 13:57
2
1
Bunuel wrote:

GMAT Club Tests Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

This is an Alternative approach.

(1) So x^x must equal 1 or -1. This can happen if the exponent is 0 which is impossible by question definition or if x = 1 or if x = -1.
That is, 1^1 = 1 and -1^-1 = -1 so in absolute value both equal 1.
Insufficient.

(2) If we're not sure where to start we'll try easy numbers. If x = 1 then 1^5 = 1^1 = 1 so x = 1 works. If x = 2 then 2^5 = 32 but 2^2 = 4 so x = 2 doesn't work. Since the exponent on the left is 5 it makes sense to try x = 5 which gives 5^5 = 5^5. So x = 1 and x = 5 both work.
Insufficient.

Combined:
x = 1 fits both criteria as shown above. How about x = -1? -1^5 = -1 and -1^-1 = -1. So both x = 1 and x = -1 fit both criteria.
Insufficient.

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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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20 May 2018, 14:03
1

St1: X=1 or x=-1
St2: x=1 or x=-1

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Joined: 02 Sep 2009
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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24 Dec 2018, 03:10
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

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Joined: 21 Jan 2018
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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03 Jan 2019, 10:25
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

Hi Bunuel Sir.... Can you let me what is the mistake in my method .
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File comment: My method of solving the question.

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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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03 Oct 2019, 08:11
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

as per statement 2 .. can we not use the common base concept ?? then x=5 would be the answer and would be sufficient ??
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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03 Oct 2019, 18:06
1
vamkrispk wrote:
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

as per statement 2 .. can we not use the common base concept ?? then x=5 would be the answer and would be sufficient ??

We have to think outside of the box for this one. The base here can be x =1 and any exponent of 1 is still 1. Similarly for -1, as long as the exponents are both even/odd.
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If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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Updated on: 13 Oct 2019, 21:51
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

Analyzing the question:

We are playing around with exponents of exponents. When evaluating exponents we want to keep a few special cases in mind and test them out: The exponent being 0 or 1, the base being 0 or 1. Here we should also test -1 since we see absolute values.

Statement 1:
x = 1 or x = -1 satisfy this, insufficient.

Statement 2:
This one is a little tricky, x = 5 and x = 1 both satisfy this equation. Since 5 is an odd exponent, we should test out x=-1 as well, which works.

Combined:
x = 1 or x = -1 satisfy both statements, insufficient.

Ans: E
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Originally posted by TestPrepUnlimited on 03 Oct 2019, 18:13.
Last edited by TestPrepUnlimited on 13 Oct 2019, 21:51, edited 2 times in total.
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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07 Oct 2019, 22:56
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

(1) $$|x^x| = 1$$
x = 1 or x = -1
NOT SUFFICIENT

(2) $$x^5 = x^x$$[/quote]
x = 1 or x = -1 or x=5
NOT SUFFICIENT

(1) + (2)
(1) $$|x^x| = 1$$
x = 1 or x = -1
(2) $$x^5 = x^x$$[/quote]
x = 1 or x = -1 or x=5
x = 1 or x = -1
NOT SUFFICIENT

IMO E
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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17 Oct 2019, 05:38
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$
(2) $$x^5 = x^x$$

(1) $$|x^x| = 1$$: insufic.

$$|x^x| = 1…x=1…|1^1|=1$$
$$|x^x| = 1…x=-1…|-1^{-1}|=1$$

(2) $$x^5 = x^x$$: insufic.

$$x=1: x^5 = x^x…1^5=1^1…1=1…|1^1|=1$$
$$x=-1: x^5 = x^x…-1^5=-1^{-1}…-1=-1…|-1^{-1}|=1$$

(1&2): insufic.

$$x=1: x^5 = x^x…1^5=1^1…1=1…|1^1|=1$$
$$x=-1: x^5 = x^x…-1^5=-1^{-1}…-1=-1…|-1^{-1}|=1$$

Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x   [#permalink] 17 Oct 2019, 05:38